Finite Group Databasebeta

C2×#13115642 #15866544

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#13115642

Splittings

FittingC22×C4×C8×C13 ⋊ C2
SylowC13 ⋊ C2×#1957

Subgroups

subgroupG/H
centerC24C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C4×C8×C13C2
socleC24×C13C2×D4
prime radicalC22×#88128C2
cosocleC22×C4×C13C24
hypercenterC22×C4×C8D13
hypocenterC13C2×#1957
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×C8

2414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 173193);